Gordon Strachan's men sit rock bottom of Group A with their hosts vying with Belgium for top spot - and they will have to do without the Celtic captain for one of the toughest fixtures in the campaign.
The news will be of particular concern to Bhoys manager Neil Lennon, with Champions League qualifying kicking off early next season.
Strachan said: "He has to call it a day for a while. I think I'll leave it to Celtic to tell you how long it is going to be because it is not my right to tell you.
"I spoke to Broony for a long time this week but it had nothing to do with football, I just spoke to Broony for a long time. I think it is up to Celtic to tell you exactly what is going on. It's only fair.
"It is a huge disappointment to lose him. Last weekend, every time Hibs had a move he would stop it. I don't think he is a natural sitter but he can do it through sheer energy."
Other absentees include Brown's club-mate James Forrest, Brighton midfielder Liam Bridcutt, Wigan's Gary Caldwell, Rangers' Lee Wallace and Southampton's Danny Fox - and Motherwell starlet Steven Hammell has been called in.
Strachan added: "I said to Mark (McGhee) and Stuart (McCall) the other day, why don't we get someone in who, when we bring them in, thinks: 'this is the best thing that's ever happened to me'. With his initial reaction I think we have found someone in Stevie Hammell."